Vertical dynamics of a single-span beam subjected to moving mass-suspended payload system with variable speeds

This paper presents the vertical dynamics of a simply supported Euler-Bernoulli beam subjected to a moving mass-suspended payload system of variable velocities. A planar theoretical model of the moving mass-suspended payload system of variable speeds is developed based on several assumptions: the rope is massless and rigid, and its length keeps constant; the stiffness of the gantry beam is much greater than the supporting beam, and the gantry beam can be treated as a mass particle traveling along the supporting beam; the supporting beam is assumed as a simply supported Bernoulli-Euler beam. The model can be degenerated to consider two classical cases-the moving mass case and the moving payload case. The proposed model is verified using both numerical and experimental methods. To further investigate the effect of possible influential factors, numerical examples are conducted covering a range of parameters, such as variable speeds (acceleration or deceleration), mass ratios of the payload to the total moving load, and the pendulum lengths. The effect of beam flexibility on swing response of the payload is also investigated. It is shown that the effect of a variable speed is significant for the deflections of the beam. The accelerating movement tends to induce larger beam deflections, while the decelerating movement smaller ones. For accelerating or decelerating movements, the moving mass model may underestimate the deflections of the beam compared with the presented model; while for uniform motion, both the moving mass model and the moving mass-payload model lead to same beam responses. Furthermore, it is observed that the swing response of the payload is not sensitive to the stiffness of the beam for operational cases of a moving crane, thus a simple moving payload model can be employed in the swing control of the payload.